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This learn node points to the page here at MIT Open Courseware for digital tools like the one illustrated above called Curves in Two Dimensions. There are more than two dozen tools for topics ranging such as precalculus, algebra and vectors, curves, surfaces and differential equations. In the MIT course with tools like the one shown are chapter outlines like this one called Curves about, as the Introduction explains:

“The tools of calculus developed so far allow us to describe most of the important properties of a smooth curve: which are its direction at any point, and how much it deviates from straightness there. This is measured by its curvature. How its path differs from planarity is measured by its torsion, also easily calculated.”

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This learn node cluster math help available online virtually from an amazing array of open sources. The picture here of Wolfgang Pauli and Niels Bohr as they “stare in wonder at a spinning top” is from lectures by David Tong of Cambridge University on Classical Dynamics. The picture is included in the third Tong lecture titled The Motion of Rigid Bodies. Pauli and Bohr � great mathematicians of the early 20th century � would surely turn the full intensity of their wonder on how a click of a 21st century mouse sends students to math help, math problems and math mentors.

In a click or two this learn node crosses the Atlantic pond from Cambridge to MIT for Algebra I lectures or to a place to think about geometry themes and variations while listening to some Bach.

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